This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A287383 #26 Apr 29 2019 05:19:12
%S A287383 1,1,1,1,1,1,1,1,1,90720,1,1,1,14968800,40864824000,1,1,453600,
%T A287383 5108114880,131993382447360,3463115239584000000
%N A287383 Triangle read by rows: T(n,m) is the number of inequivalent n X m matrices under action of the Klein group, with one-ninth each of 1's, 2's, 3's, 4's, 5's, 6's, 7's, 8's and 9's (ordered occurrences rounded up/down if n*m != 0 mod 9).
%C A287383 Computed using Polya's enumeration theorem for coloring.
%H A287383 María Merino, <a href="/A287383/b287383.txt">Rows n=0..34 of triangle, flattened</a>
%H A287383 M. Merino and I. Unanue, <a href="https://doi.org/10.1387/ekaia.17851">Counting squared grid patterns with Pólya Theory</a>, EKAIA, 34 (2018), 289-316 (in Basque).
%F A287383 G.f.: g(x1,x2,x3,x4,x5,x6,x7,x8,x9) = (y1^(m*n) + 3*y2^(m*n/2))/4 for even n and m; (y1^(m*n) + y1^n*y2^((m*n-m)/2) + 2*y2^(m*n/2))/4 for odd n and even m; (y1^(m*n) + y1^m*y2^((m*n-n)/2) + 2*y2^(m*n/2))/4 for even n and odd m; (y1^(m*n) + y1^n*y2^((m*n-n)/2) + y1^m*y2^((m*n-m)/2) + y1*y2^((m*n-1)/2))/4 for odd n and m; where the coefficients y1 and y2 correspond to y1 = Sum_{i=1..9} x_i and y2 = Sum_{i=1..9} x_i^2. Occurrences of numbers are ceiling(m*n/9) for the first k numbers and floor(m*n/9) for the last (9-k) numbers, if m*n = k mod 9.
%e A287383 For n = 3 and m = 3 the T(3,3) = 90720 solutions are colorings of 3 X 3 matrices in 9 colors inequivalent under the action of the Klein group with exactly 1 occurrence of each color (coefficient of x1^1, x2^1, x3^1, x4^1, x5^1, x6^1, x7^1, x8^1, x9^1).
%e A287383 Triangle begins:
%e A287383 ===================================================================
%e A287383 n\m | 0 1 2 3 4 5
%e A287383 ----|--------------------------------------------------------------
%e A287383 0 | 1
%e A287383 1 | 1 1
%e A287383 2 | 1 1 1
%e A287383 3 | 1 1 1 90720
%e A287383 4 | 1 1 1 14968800 40864824000
%e A287383 5 | 1 1 453600 5108114880 131993382447360 3463115239584000000
%Y A287383 Cf. A283435, A286892, A287020, A287021, A287022, A287377, A287378, A287384.
%K A287383 nonn,tabl
%O A287383 0,10
%A A287383 _María Merino_, Imanol Unanue, May 24 2017